Supplementary Material for "Mixed Fe-Mo carbide prepared by a sonochemical synthesis as highly efficient nitrate reduction electrocatalyst"

Supplementary data Experimental Section DFT All calculations were performed using spin-polarized density functional theory (DFT) as implemented in the Vienna ab initio simulation package (VASP).[1-3] The PerdewBurke-Emzerhof (PBE) functional with a plane-wave cutoff energy of 500 eV was used. For structural optimizations, the Brillouin zone was sampled using a 5 × 5 × 1 k-point grid based on the Monkhorst-Pack scheme, centered at Gamma. A vacuum space of 1.5 nm in the z direction (perpendicular to the basal plane) was used to avoid interactions between periodic images. The convergence criteria for the force on each atom was set to 0.02 eV/Å, while the electronic structure energy convergence criteria was 10-5 eV. The Grimme D3 method with Becke-Johnson parameters[4] were employed to account for Van der Waals interactions.[5] The vibrational modes were calculated at 298.15 K to obtain the zero-point energy, entropy, and temperature corrections to enthalpy. The coupled proton-electron transfer (CPET) reactions were modelled using the computational hydrogen electrode (CHE) of Norskov.[6] In this approach, the voltage of reference (zero) is defined as for the reversible hydrogen electrode (RHE), where gas-phase hydrogen is converted into protons and electrons (reversibly) at zero volts (H+ + e– → ½ H2). Because this reaction is in equilibrium, one can make the approximation that the chemical potential of the proton-electron pair, μ(H+) + μ(e-), equals half of the chemical potential of gas-phase H2, 1/2μ(H2). This last quantity can be trivially approximated via DFT calculations. As result, the chemical potential of the proton-electron pair can be adjusted based on the applied potential (U) with the equation (1): μ(H+) + μ(e-) → 1/2μ(H2) – eU (1) where e is the elementary positive charge. It is assumed that both proton and electron transfer occur in concert during an electrochemical step. For all of the electrochemical steps along the reaction path, the free energy change between intermediates was computed to indicate the feasibility of the electrochemical process, i.e., no energy barriers were calculated. Based on the computational hydrogen electrode (CHE) model, the Gibbs free energy change (ΔG) was calculated using Equation (2): ∆𝐺 = ∆𝐸𝐷𝐹𝑇 + ∆𝐸𝑍𝑃𝐸 − 𝑇∆𝑆 + 𝑘𝑇𝑙𝑛10 𝑥 𝑝𝐻 −𝑒𝑈 (2) where ∆𝐸𝐷𝐹𝑇 is the total energy from DFT simulations, ∆𝐸𝑍𝑃𝐸 is the zero-point energy calculated from vibrational frequencies, T is the temperature (298.15 K), S is the entropy obtained from vibrational frequencies, k is the Boltzmann constant, and U is the electrode potential. Note that EZPE and S can be directly obtained from frequency calculations using VASPKIT.[7] We expect that the proton transfer from the solution to the adsorbates has low barriers, especially under negative potential. Gasor liquid-phase errors associated with H2O, HNO3 and NH3 were corrected based on the method developed by Granda-Marulanda et al.[8] To avoid calculating the charged molecule NO3-, the Gibbs free energy of aqueous NO3was derived from those of gaseous HNO3 and H2. Therefore, a correction for solvation (∆𝐺𝑠𝑜𝑙) should be added to the *NO3 energy value, and it has been reported to be equal to 0.392 eV.[9] ∆𝐺∗𝑁𝑂3 𝑐𝑜𝑟𝑟 = ∆𝐺∗𝑁𝑂3+ ∆𝐺𝑠𝑜𝑙 = ∆𝐺∗𝑁𝑂3+ 0.392 (3) Similarly, the adsorption energy for NO3 has been computed considering the same correction: ∆𝐺∗𝑁𝑂3 𝑎𝑏𝑠 = 𝐺∗𝑁𝑂3− 𝐺∗− 𝐺𝐻𝑁𝑂3 +1 2𝐺𝐻2 + 0.392 (4) The d band center (ℇd) for the metal atom involved in the catalysis around the adsorption sites is given by 𝜀𝑑= ∫𝜌(𝐸)(𝐸−𝐸𝐹) 𝑑𝐸 +∞ −∞ ∫(𝐸−𝐸𝐹) 𝑑𝐸 +∞ −∞ (5) where ρ(E) is the density of state (DOS) projected on the d-states of the metal atoms and EF is the Fermi energy of the system. Bader charge analysis was considered to quantify the charge transfer of selected intermediates. Product quantification The evolving gases were analyzed with an Agilent 490 Micro GC system (Molsieve 5 Å column using Ar as carrier gas). N-containing species were detected by colorimetry with ultraviolet-visible (UV-Vis) spectrophotometer. In particular, NH3 was also quantified by the solution 1H NMR spectroscopy method. In detail, 400 µL of electrolyte and 100 uL of 1M H2SO4 were mixed with 100 µL deuterium oxide containing a known concentration DMSO as the internal standard. Determination of ammonia The concentration of produced ammonia was spectrophotometrically detected by the Nessler’s reagent method. Due to the large concentration of ammonia, the electrolyte after 1 h of electrolysis was diluted by 20-50 times to reach the detected range. Then, 5 mL of the diluted electrolyte, 0.2 mL of a 1 M NaOH solution with 5% salicylic acid and 5% sodium citrate, 0.5 mL of 0.05 M NaClO and 0.2 mL of 1% sodium nitroferricyanide (III) dihydrate (C5FeN6Na2O·2H2O) solution were mixed. After standing in the dark for 3 h, the concentration of indophenol blue was detected by an ultraviolet-visible (UV-Vis) spectrophotometer at a wavelength of 635 nm in the absorption spectrum. Determination of NO2– The Griess test was adopted to evaluate the concentration NO2in electrolyte. Firstly, the Griess reagents were prepared by adding 0.1 g N-(1-naphthyl)-ethylenediamine dihydrochloride, 1.0 g sulfonamide and 2.94 mL H3PO4 in 50 mL deionized water. 5 mL electrolyte after diluting by adding deionized water, and then 0.1 mL chromogenic agent was added. After standing for 20 minutes, the absorbance curve was measured in the wavelength range of 400-700 nm and the absorbance value of 540 nm was selected. A series of NaNO2 solutions with different concentrations were used to determine the standard curve. Determination of N2H4 Hydrazine in the electrolytes was detected by the Watt-Chrisp method. A mixture of ethanol (100 mL), para(dimethylamino) benzaldehyde (2.0 g) and HCl (concentrated, 12 mL) were used as a color reagent. 2 mL color reagent was added into 2 mL of diluted electrolyte. After 30 min, the absorbance was measured at a wavelength of 458 nm. The standard hydrazine monohydrate solutions with the given concentrations of hydrazine in 0.2 M K2SO4 were also prepared for building the calibration curves. SUPPORTING FIGURES AND TABLES Fig. S1 PXRD patterns of (a) FC/CB and FC, and (b) MC/CB and MC. Fig. S2. TEM image of FMC. Fig. S3. SEM images of FMC (a-c) and FMC/CB (d-f) at different magnifications. Fig. S4. (a) TEM image of MC/CB and corresponding nanoparticle size distribution histrogram; (b) high resolution TEM image of MC/CB and its lattice fringes. Fig. S5 (a) TEM image of FC/CB and corresponding nanoparticle size distribution histogram; (b) high resolution TEM image of FC/CB and its lattice fringes. Fig. S6. Elemental mapping of FMC/CB. Fig. S7. Experimental XPS Fe 2p peak of FMC/CB and FC/CB. Fig. S8. The EXAFS fitting curves of FMC at R space. Fig. S9 The EXAFS fitting curves of FMC at k space. Fig. S10 The electrochemically active surface area (ECSA) of different samples based on the double-layer capacitance. Fig. S11. (a) UV-Vis absorption spectra of the NH3 standard solution at different concentrations. (b) Linear relationship between the light absorbance at 635 nm and the concentration of NH3 standard solution. Fig. S12. (a) UV-Vis absorption spectra of the NO2standard solution at different concentrations. (b) Linear relationship between the light absorbance at 540 nm and the concentration of NO2standard solution. Fig. S13 A representative 1H NMR spectrum for NH3 quantification recorded using water suppression mode. References. [1] P.E. Blöchl, Projector augmented-wave method, Physical review B, 50 (1994) 17953. [2] G. Kresse, J. 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